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The Relevance Research Of Geometric Proving Level And Mathematical Achievement Of Ninth Graders

Posted on:2017-06-03Degree:MasterType:Thesis
Country:ChinaCandidate:L YuFull Text:PDF
GTID:2347330485496684Subject:Subject teaching
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Under the background of curriculum reform, many changes have been occurred to geometric courses' content arrangement and setting. However, the problems of geometric teaching doesn't benefit from the curriculum reform. In practical teaching, lots of math teachers find out that some students do not have any cognitive disorder in understanding the geometric knowledge, but at the same time, they could not answer correctly in the proof questions, which indicates that students have problem in transferring form geometric cognitive structure to thinking structure, that means the students' geometric thinking abilities are not matching with their geometric proving abilities.Based on the Van Hiele levels of geometric thought and SOLO taxonomy theory, this article mainly uses quantitative research method and firstly proposes that geometric proving levels can be divided as: Level 1 – intuitional proving, Level 2 – descriptive proving, Level 3 – relevant proving, Level 4 – logical proving, Level 5 – optimized proving. Then integrated junior school teaching materials and ?Curriculum Standards(Version 2011)?, test papers of geometric proving level have been drawn up and the relevant evaluation index has been set. 191 ninth graders from a middle school in Guangzhou are selected as research samples. Under the data statistics of relevant tests, this article not only discusses the ninth graders' distribution of geometric thinking level and geometric proving level, but also studies the relevance between students' geometric thinking level and proving level, geometric proving level and mathematics achievements.The main conclusions are as follows:1. 12% students' geometric thinking are under Level 3, more than 80% students are at Level 3 or above. It's unevenly distributed in general. The data from Level 1 to Level 4 is 3.8%, 8.2%, 66.5%, 14.3%. Another 7.1% students deviates from the Van Hiele theory. It shows no difference between boys and girls in the development of geometric thinking level.2. 16% students are still in low geometric proving level, 32% are in middle geometric proving level and more than 50% reach high geometric proving level. It's unevenly distributed in general. The data from Level 1 to Level 5 is 3.3%, 12.64%, 32.42%, 42.86%, 8.79%. Boys and girls also have no difference in the development of geometric proving level.3. Comparison between geometric thinking level and geometric proving level indicates that they have certain relevance. Different Van Hiele geometric thinking level corresponds to several different geometric proving level and transfers to relevant geometric proving levels according to a certain proportion.4. There's strongly positive correlation between geometric thinking level and geometric proving level, the Spearman correlation coefficient of them is 0.822. There's strongly positive correlation between geometric proving level and their mathematics achievements of Model Test 1 and the high school entrance exam, the Spearman correlation coefficient of them is 0.937 and 0.956.Based on the research conclusions, the author carries on a cognitive analysis of different geometric proving level students, proposes a hierarchical structure and corresponding characteristics of geometric proving level and give teaching suggestions to students of different geometric proving levels: 1. Against the students of low geometric proving level, reading practices and graph recognition and identification practices should be strengthened. Teachers should offer detailed blackboard writing for the students to imitate and learn. 2. Against the students in middle geometric proving level, the mind mapping method should be used to let the students write down the proof thinking analysis so as to give a systemic vision of their geometric knowledge. 3. Against the students in high geometric proving level, attentions should be paid on the induction of geometric learning methods. The teachers should give specific guidance and encourage when the students raise new questions after the original question is solved.This article aims at providing valuable reference base to mathematics course reform, teaching materials writing and teachers' teaching, so as to prompt the teachers to use modern education concept more scientifically and efficiently and enhance classroom teaching.
Keywords/Search Tags:The Van Hiele Levels of Geometric Thought, SOLO Taxonomy Theory, Geometric Proof, Math of Ninth Grade
PDF Full Text Request
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